If you asked 100 college-educated people to explain WHY 7 x 5 = 35, I'll be that 90 of them couldn't give you a remotely satisfactory answer.

Makes no sense

What doesn't make sense? People know that 7 x 5 = 35, but in most cases it is only because they memorized a multiplication table when they were in first grade. In other words, they think of it as an absolute fact, and could not prove that 7 x 5 = 35 (or even provide some basic intuition as to why it is true). This point becomes obvious when you change traditional math problems in trivial ways; for example, lots of people would be stumped if you asked them what (7/35) x 5 is, because they have no conceptual understanding of basic mathematical operations. A majority of college students would pull out a calculator to solve that problem.

This is 100 percent correct. I wrote up an exam in which a calculator WOULD NOT help you (solutions were in symbolic algebra form; interm. macro, btw) and students STILL asked me if they could bring their calculators as a security blanket, lol. NOPE

The real exam was simply the practice exam but with different numbers for some the given information. I went over the practice exam and gave all the solutions and answered all questions about it. Many, many students failed the ream exam. I fear for future generations.

These students are probably above the population mean in terms of intelligence, ability, and likelihood to have a reasonably successful career. Next time you go into a bank, airport, government agency, or somewhere else where you really rely on the competence of others, think how few of them could succeed at that exam. And try not to cry with fear.

The world is full of people who seem intelligent and are reasonably successful. But if you really got into it with them, you would realize how dumb they are.

- Punishing students, who both didn't study AND don't understand the material

- Equating smart students who understand the material with dumb students who don't understand material, but did the practice exam

I wouldn't be particularly proud if I was you

The real exam was simply the practice exam but with different numbers for some the given information. I went over the practice exam and gave all the solutions and answered all questions about it. Many, many students failed the ream exam. I fear for future generations.

I think the general point to be made here is that most students approach mathematical topics in completely the wrong way, largely because they've been taught incorrectly their entire lives. So much of primary and secondary education is taken up be teaching kids to memorize stuff, with no regard for obtaining a conceptual understanding of the material. If you asked 100 college-educated people to explain WHY 7 x 5 = 35, I'll be that 90 of them couldn't give you a remotely satisfactory answer.

That's a s**t question honestly. The "right" answer completely depends on your expectations. You could say that if I line up five stacks of seven coins and then count the total amount of coins, I would arrive at 35. Or I could talk about the ring axioms that define multiplication over whole numbers.

I'm a US tenured prof making 180K a year in a private university (my Dept is LRM though). I only teach 3 courses a year (2 of them undergraduate), and I can tell you this: NOBODY gives a sh!t. Remember that our society requires people to provide customer support over the phone, bank tellers, realtors, as well as other roles. They won't use what you teach them (at least the majority of them), so why feeling this way. In my 15-years long academic career, the only people I cared about (apart from myself) are perhaps about 20 (amazing kids!). I wrote letters of recommendation for grad school and serve as their reference for job applications, etc. They are doing amazing. Some became academics themselves, others have climbed the corporate ladder rather quickly and have successful careers. Do I care about the other 2000 over kids, nah. Some people need to take my credit card payment over the phone.

unfortunately, the phone tellers are having secks with your gf behind your back. Some have become successful plumbers who earn 200k or more. Some migrated to Canada and started as drivers and earned about 150k. Some started at big 4 firms and slowly progressed to where the top 20 were at maybe taking two or three years more. Some became drug addicts and lived fast and died young. Some enjoyed life and banged more women than you could still buy with your 180k. Meanwhile, you live your sad life, hoping two or three people a year read what you have written. Your life is devoid of any happiness sans the emotions you feel looking out of your office, hoping that one day you could get tenure at an HRM, have a family with two beautiful kids and a wife who understands you. Your life is a lie.

I'm a US tenured prof making 180K a year in a private university (my Dept is LRM though). I only teach 3 courses a year (2 of them undergraduate), and I can tell you this: NOBODY gives a sh!t. Remember that our society requires people to provide customer support over the phone, bank tellers, realtors, as well as other roles. They won't use what you teach them (at least the majority of them), so why feeling this way. In my 15-years long academic career, the only people I cared about (apart from myself) are perhaps about 20 (amazing kids!). I wrote letters of recommendation for grad school and serve as their reference for job applications, etc. They are doing amazing. Some became academics themselves, others have climbed the corporate ladder rather quickly and have successful careers. Do I care about the other 2000 over kids, nah. Some people need to take my credit card payment over the phone.

If you asked 100 college-educated people to explain WHY 7 x 5 = 35, I'll be that 90 of them couldn't give you a remotely satisfactory answer.

Makes no sense

What doesn't make sense? People know that 7 x 5 = 35, but in most cases it is only because they memorized a multiplication table when they were in first grade. In other words, they think of it as an absolute fact, and could not prove that 7 x 5 = 35 (or even provide some basic intuition as to why it is true). This point becomes obvious when you change traditional math problems in trivial ways; for example, lots of people would be stumped if you asked them what (7/35) x 5 is, because they have no conceptual understanding of basic mathematical operations. A majority of college students would pull out a calculator to solve that problem.

This is 100 percent correct. I wrote up an exam in which a calculator WOULD NOT help you (solutions were in symbolic algebra form; interm. macro, btw) and students STILL asked me if they could bring their calculators as a security blanket, lol. NOPE

"This class would be easier if you just used numbers like the real world!"

Let's see what you achieved with this move:
- Punishing students, who both didn't study AND don't understand the material
- Equating smart students who understand the material with dumb students who don't understand material, but did the practice exam

- Providing students an opportunity to recognize their gaps in understanding and remedy them, then asking questions that would have rewarded that course of action. Talented students do well. Students who understand the material do well. "Dumb" students who take the time to remedy their dumbth do well. Students who don't get the material and either didn't prepare or didn't use the feedback the exam gave them do poorly.

I had an econometrics professor do this when I was an undergrad. I felt like I was the only student who noticed. Although I got 100% on all the exams, I feel like I wasn't challenged and didn't learn as much because, after the first exam, I only studied the practice exam.

Now on the other side, I see the wisdom in this strategy (minimal work for the professor).

A similar thing happens to me when I just give them the same test without changing anything.